"We study the stochastic dynamics of evolutionary games, and focus on the so-called `stochastic slowdown' effect, previously observed in (Altrock et. al, 2010) for simple evolutionary dynamics. Slowdown here refers to the fact that a beneficial mutation may take longer to fixate than a neutral one. More precisely, the fixation time conditioned on the mutant taking over can show a maximum at intermediate selection strength. We show that this phenomenon is present in the prisoner's dilemma, and also discuss counterintuitive slowdown and speedup in coexistence games. In order to establish the microscopic origins of these phenomena, we calculate the average sojourn times. This allows us to identify the transient states which contribute most to the slowdown effect, and enables us to provide an understanding of slowdown in the takeover of a small group of cooperators by defectors: Defection spreads quickly initially, but the final steps to takeover can be delayed significantly. The analysis of coexistence games reveals even more intricate behavior. In small populations, the conditional average fixation time can show multiple extrema as a function of the selection strength, e.g., slowdown, speedup, and slowdown again. We classify two-player games with respect to the possibility to observe non-monotonic behavior of the conditional average fixation time as a function of selection strength."

"Without mutation and migration, evolutionary dynamics ultimately leads to the extinction of all but one species. Such fixation processes are well understood and can be characterized analytically with methods from statistical physics. However, many biological arguments focus on stationary distributions in a mutation-selection equilibrium. Here, we address the equilibration time required to reach stationarity in the presence of mutation, this is known as the mixing time in the theory of Markov processes. We show that mixing times in evolutionary games have the opposite behaviour from fixation times when the intensity of selection increases: In coordination games with bistabilities, the fixation time decreases, but the mixing time increases. In coexistence games with metastable states, the fixation time increases, but the mixing time decreases. Our results are based on simulations and the WKB approximation of the master equation."

"Cooperation and the allocation of common resources are core features of social behavior. Games idealizing both interactions have been studied separately. But here, rather than examining the dynamics of the individual games, the interactions are combined so that players first choose whether to cooperate, and then, if they jointly cooperate, they bargain over the fruits of their cooperation. It is shown that the dynamics of the combined game cannot simply be reduced to the dynamics of the individual games and that both cooperation and fair division are more likely in the combined game than in the constituent games taken separately."

In a public form, at last.

"Finite-size fluctuations in coevolutionary dynamics arise in models of biological as well as of social and economic systems. This brief tutorial review surveys a systematic approach starting from a stochastic process discrete both in time and state. The limit $N\to \infty$ of an infinite population can be considered explicitly, generally leading to a replicator-type equation in zero order, and to a Fokker-Planck-type equation in first order in $1/\sqrt{N}$. Consequences and relations to some previous approaches are outlined."

"In this review, we summarize recent developments in stochastic evolutionary game dynamics of finite populations." Looks decent, at first scan.

"A model of “ephemeral” population structure is pre- sented that applies not only to biological systems in which discrete groups form but also to networks without group boundaries. The evolution of altruistic behaviors is discussed. Nonrandom interaction and nonlinear fitness structures are modeled; together, these factors can produce stable polymorphisms of altruistic and selfish types, as well as bistability. Empirical applications of the model may be found in microbes, marine invertebrates, annual plants, and other organisms."

"We study repeated games where players use an exponential learning scheme in order to adapt to an ever-changing environment. If the game’s payoffs are subject to random perturbations, this scheme leads to a new stochastic version of the replicator dynamics that is quite different from the “aggregate shocks” approach of evolutionary game theory. Irrespective of the perturbations’ magnitude, we find that strategies which are dominated (even iteratively) eventually become extinct and that the game’s strict Nash equilibria are stochastically asymptotically stable. We complement our analysis by illustrating these results in the case of congestion games."

"Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist... Both biotic interactions and environmental fluctuations ... can facilitate or disrupt coexistence. To better understand this interplay between these deterministic and stochastic forces, we develop a mathematical theory extending the nonlinear theory of permanence for deterministic systems to stochastic difference and differential equations. Our condition for coexistence requires that there is a fixed set of weights associated with the interacting populations and this weighted combination of populations' invasion rates is positive for any (ergodic) stationary distribution associated with a subcollection of populations. ... with] sufficient noise ... the populations approach a unique positive stationary distribution. ... coexistence criterion is robust to small perturbations of the model functions."

"The joint dynamics of population-level social institutions and individual preferences (or more broadly cultures) are illustrated in four case studies: the end of Communist Party rule in the German Democratic Republic, the transformation of traditional contracts governing agricultural work in the Philippines, the demise of Apartheid in South Africa, and the spread and retreat of female genital cutting in West Africa. A stochastic evolutionary game model of the underlying processes captures five interrelated aspects of real world historical dynamics: its often bottom- up and decentralized nature, the complementarity between cultural and institutional dynamics, the long term persistence of inefficient institutions, the often revolutionary nature of institutional and cultural change and the prominent role of technical change in the process of institutional and cultural innovation." --- Do I detect, comrades, in that last sentence, an echo of "in the last instance"?

A cute use of averaging techniques --- start with replicator equations with time-dependent perturbations to the fitness function, and replace them with different, time-independent replicator equations with a different fitness function. I think the particular averaging trick they use here will break down if the perturbations are not strictly periodic...

"Flesch integrates evolutionary psychology into literary studies, creating a new theory of fiction in which form and content flawlessly intermesh. Fiction, Flesch contends, gives us our most powerful way of making sense of the social world. Comeuppance begins with an exploration of the appeal of gossip and ends with an account of how we can think about characters and care about them as much as about persons we know to be real. We praise a storyteller who contrives a happy or at least an appropriate ending, and fault the writer who refuses us one. Flesch uses Darwinian theory to show how fiction satisfies our desire to see the good vindicated and the wicked get their comeuppance." --- This would seem to have so many obvious counterexamples that I want to read the book just to watch the train-wreck.

"replicator equations (RE) are among the basic tools in mathematical theory of selection and evolution. We develop a method for reducing a wide class of the RE, which in general are systems of differential equations in Banach space to escort systems of ODEs that in many cases can be explored analytically. The method has potential for different applications; some examples are given."

- The method does not seem to apply when fitness fluctuates stochastically.

"We propose that microbes that have developed persistent relationships with human hosts have evolved cross-signalling mechanisms that permit homeostasis that conforms to Nash equilibria and, more specifically, to evolutionarily stable strategies. This imp